Background Individuals with intellectual disabilities are at increased risk of becoming overweight or obese. This is particularly evident in people with trisomy 21 and Prader–Willi syndrome (PWS). Although metabolic factors are known to contribute to obesity in trisomy 21 and hyperphagia plays a primary role in PWS, hyperphagia has not yet been investigated as a possible contributing factor to obesity in trisomy 21. Methods Participants comprised three diagnostic groups: trisomy 21 (T21 group), PWS (PWS group) and lifestyle‐related obesity (LRO group). They were required to be aged 6–18 years and have a body mass index over the 85th percentile for age and gender. A parent of each participant completed the Hyperphagia Questionnaire and the Children's Leisure Activity Study Survey. Mean scores for each domain and across all domains of the Hyperphagia Questionnaire and the Children's Leisure Activity Study Survey were compared between diagnostic groups using linear regression analysis. Results The study group consisted of 52 young people (23 men and 29 women) aged 6–18 years (mean 12.5 years; T21 group n = 17, PWS group n = 16 and LRO group n = 19). As hypothesised, the PWS group had the highest mean scores across all domains of the Hyperphagia Questionnaire, and the LRO group had the lowest. Food‐seeking behaviour was more pronounced in the PWS group than the T21 group (mean score 13.2 vs. 8.6, p = 0.008). The LRO group spent more hours per week engaged in physical activity (14.7) in comparison with the other groups (9.6 and 9.7), whereas between the groups, differences in time spent in sedentary activities were less pronounced. Conclusions Preoccupation with food and low levels of physical activity may contribute to the development of overweight and obesity in some individuals with trisomy 21. These factors warrant consideration in the clinical context.